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The valence of harmonic polynomials
Author(s):
A.
S.
Wilmshurst
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2077-2081.
MSC (1991):
Primary 30C55
MathSciNet review:
1443416
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Abstract:
The paper gives an upper bound for the valence of harmonic polynomials. An example is given to show that this bound is sharp.
References:
- 1.
- J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. MR 85i:30014
- 2.
- F. Kirwan, Complex Algebraic Curves, Cambridge University Press (1992). MR 93j:14025
- 3.
- A. Lyzzaik, On the valence of some classes of harmonic maps, Math. Proc. Cambridge Philos. Soc. 110 (1991), 313-325. MR 92f:31001
- 4.
- -, Local properties of light harmonic mappings, Canad. J. Math. 44 (1992), 135-153. MR 93e:30048
- 5.
- T. Sheil-Small, On the Fourier series of a finitely described convex curve and a conjecture of H. S. Shapiro, Math. Proc. Cambridge Philos. Soc. 98 (1985), 513-525. MR 86m:42009
- 6.
- A. S. Wilmshurst, Complex harmonic mappings and the valence of harmonic polynomials, D. Phil. thesis, University of York, England, 1994.
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Additional Information:
A.
S.
Wilmshurst
Affiliation:
Department of Mathematics, University of York, York Y01 5DD, England
DOI:
10.1090/S0002-9939-98-04315-9
PII:
S 0002-9939(98)04315-9
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1998,
American Mathematical Society
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